calculus

posted by .

A triangle ABC has sides of length AB = 3 inches and AC = 4 inches. Let t denote the angle at vertex A, and let s denote the length of the remaining side BC. If t increases at the rate of 2 radians per second, at what rate (in inches per second) does s change at the instant when t is a right angle? [Hint: You will need to use the Law of Cosines.]

  • calculus -

    s^2 = 3^2 + 4^2 - 2(3)(4)cos T
    2s ds/dt = 24sin T dT/dt
    s ds/dt = -12sin T dT/dt

    when T = 90°, s = 5, sinT = 1 , dT/dt = 2 rad/sec

    5 ds/dt = -12(1)(2)
    ds/dt = -24/5 = -4.8 inches/sec

    at that precise instant, the third side is decreasing at 4.8 inches/sec

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. geometry

    Right triangle ABC is similar to triangle XYZ, because angle B is congruent to angle Y. If side AB equals 12 inches, side BC equals 27 inches, and side YZ equals 9 inches, then what is the length of side XY?
  2. geometry

    Right triangle ABC is similar to triangle XYZ, because angle B is congruent to angle Y. If side AB equals 15 inches, side BC equals 45 inches, and side YZ equals 9 inches, then what is the length of side XY?
  3. geometry

    The sum of the lengths of the sides of triangle ABC is 25 in. The lengths of sides AB and BC are 9 inches and 8 inches. Find the length of side AC and classify the triangle.
  4. Math

    The sum of the lengths of the sides of triangle ABC is 38in. The length of sides AB and BC are 14 inches and 11 inches. Find the length of side AC and classify the triangle.
  5. Math

    Right triangle ABC is similar to triangle XYZ. If the length of side AB is 30 inches, the length of side BC is 60 inches, and the length of side YZ is 10 inches, what is the length of side XY?
  6. Math

    In a triangle ABC, with angles A, B, and C and sides AB, BC, and AC, angle B is a right (90°) angle. If the sin of angle A is 0.5 and side BC is 8 inches long, what is the length of side AC?
  7. math

    In triangle ABC, the length of side AB is 10 inches and the length of side BC is 19 inches. Which of the following could be the length of side AC?
  8. math

    The sides of a triangle are in the extended ratio 2 6 7. If the perimeter of the triangle is 45 inches, then what is the length of the shortest side?
  9. Math

    the 3 sides of a triangle have lengths of (x+7) inches, (5x+6) inches, and (5x-3) inches. What is the length of the shortest side if the perimeter of the triangle is 43 inches
  10. Math intermediate algebra

    The perimeter of a triangle is 33 inches. The sum of the length of the longest side and twice the length of the shortest side is 31 inches. Twice the length of the longest side minus the sum of the lengths of the other sides is 12 …

More Similar Questions